1. The Pew Research Center reported in 2017 that only 12% of Americans supported cuts in federal spending on Medicaid. Is the percentage smaller this year?

We tested the following hypotheses at the 5% level of significance.

H₀: This year the proportion of Americans who support federal spending cuts to Medicaid is 0.12

H_a: This year the proportion of Americans who support federal spending cuts to Medicaid is less than 0.12

The P-value is 0.026, so we reject the null hypothesis and accept the alternative hypothesis. We conclude that this year the proportion of Americans who support federal spending cuts to Medicaid is less than 0.12

What type of error is possible here?

• neither
• Type II
• both
• Type I

2. Does the potential for a Type I or Type II error change if we change the level of significance.

Suppose that we tested the same hypotheses at the 1% level of significance.

H₀: This year the proportion of Americans who support federal spending cuts to Medicaid is 0.12

H_a: This year the proportion of Americans who support federal spending cuts to Medicaid is less than 0.12

The P-value is 0.026, so we fail to reject the null hypothesis. With a 0.01 level of significance, we conclude that the sample selected this year does not provide evidence that is strong enough to support of the alternative hypothesis that the proportion of Americans who support federal spending cuts to Medicaid is less than 0.12 this year.

What type of error is possible here?

• Type I
• Type II
• neither
• both